A triangle has side lengths that are all integers. The length of one side is four times as long as the second side, and the third side has length 20. What is the largest possible perimeter of the triangle?

Question

anonymous · Answer

let this circle has sides $$a,b,c$$$$a=4x,b=x,c=20$$

anonymous · Answer

$$P(x)=20+x+4x=20+5x$$

campbell_st · Answer

there is a bit of triangle geometry that says the sum of the shorter sides of a triangle must be greater than the longer side

so if 20 is the longer side

4x + x > 20     or 5x > 20       resulting in x > 5

if 4x is the longer side

then allply the same logic

  x + 20 > 4x       or -3x > -20        or     x < 20/3

perhaps this helps... in finding the largest perimeter given you know the max and min values

anonymous · Answer

the first one results in x>4
x<20/3=6.67
so the largest x is when it is x=6(integer)
so $$P(6)=20+5(6)=50$$

anonymous · Answer

yeah its correct

anonymous · Answer

i mean $$\huge 4\le x \le 6.67,x \in Z\implies x_{max}=6$$